Question: Simplify the expression. $(r^{3}+r^{2}-4r)(-6r^{2}-3r)$
Answer: First use the distributive property. $ r^3 (-6 r^2) + r^3 (-3 r) + r^2 (-6 r^2) + r^2 (-3 r) - 4 r (-6 r^2) - 4 r (-3 r) $ Simplify. $ - 6r^{5} - 3r^{4} - 6r^{4} - 3r^{3} + 24r^{3} + 12r^{2} $ $-6r^{5}-9r^{4}+21r^{3}+12r^{2}$ Identify like terms. $ {- 6r^{5}} \color{#DF0030} {- 3r^{4}} \color{#DF0030} {- 6r^{4}} {- 3r^{3}} {+ 24r^{3}} {+ 12r^{2}} $ Add the coefficients. $ { -6r^{5}} \color{#DF0030} { -9r^{4}} {+ 21r^{3}} {+ 12r^{2}} $